Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.bl
\(\chi_{1521}(40,\cdot)\) \(\chi_{1521}(79,\cdot)\) \(\chi_{1521}(157,\cdot)\) \(\chi_{1521}(196,\cdot)\) \(\chi_{1521}(274,\cdot)\) \(\chi_{1521}(313,\cdot)\) \(\chi_{1521}(391,\cdot)\) \(\chi_{1521}(430,\cdot)\) \(\chi_{1521}(547,\cdot)\) \(\chi_{1521}(625,\cdot)\) \(\chi_{1521}(664,\cdot)\) \(\chi_{1521}(742,\cdot)\) \(\chi_{1521}(781,\cdot)\) \(\chi_{1521}(859,\cdot)\) \(\chi_{1521}(898,\cdot)\) \(\chi_{1521}(976,\cdot)\) \(\chi_{1521}(1093,\cdot)\) \(\chi_{1521}(1132,\cdot)\) \(\chi_{1521}(1210,\cdot)\) \(\chi_{1521}(1249,\cdot)\) \(\chi_{1521}(1327,\cdot)\) \(\chi_{1521}(1366,\cdot)\) \(\chi_{1521}(1444,\cdot)\) \(\chi_{1521}(1483,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) |